Theorems · Theorem · group theory

SubgroupClass.inclusion_inclusion

∀ {G : Type u_1} [inst : Group G] {S : Type u_4} {H K : S} [inst_1 : SetLike S G] [inst_2 : SubgroupClass S G]
  [inst_3 : Preorder S] [inst_4 : IsConcreteLE S G] {L : S} (hHK : H ≤ K) (hKL : K ≤ L) (x : ↥H),
  (SubgroupClass.inclusion hKL) ((SubgroupClass.inclusion hHK) x) = (SubgroupClass.inclusion ⋯) x

Defined in: Mathlib.Algebra.Group.Subgroup.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Quot.sound
Assumes: Group SetLike SubgroupClass Preorder IsConcreteLE

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DFunLike.coestatement and proof · cited by 62,936
Preorderstatement and proof · cited by 7,952
Groupstatement and proof · cited by 6,238
MonoidHomstatement · cited by 3,629
LE.le.transstatement · cited by 3,151
SetLikestatement and proof · cited by 1,084
SubgroupClassstatement and proof · cited by 34
IsConcreteLEstatement and proof · cited by 28
SubgroupClass.inclusionstatement and proof · cited by 6

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